Was bedeutet The president subscribes to this “madman theory” that if he makes a lot of unsettling, off-putting comments that sort of throw people off,, that he likes to keep his adversaries guessing ?

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1) “subscribe to” means something different than it normally does in this context. If you “subscribe to” a theory or a method of doing things, it just means you do that method or believe that theory. For example, you can say “I subscribe to the theory that hard work should be rewarded”, and that will mean you believe that hard work should be rewarded.
In this context it means that the president believes in the “madman theory” that is described later in the sentence.
2) “off-putting” is another word for “unsettling”. I can’t think of a difference.
3) “throw people off” means to confuse, interrupt, distract, or to mislead people. It basically means that you’re making it hard for someone else to understand something. For example, if you were giving a presentation and then someone shouted to interrupt you, then you’d be “thrown off” by that interruption.

Does that help?